Final answer:
To find the angle between vectors u and v, use the dot product formula and calculate the magnitudes of the vectors. The angle between u and v is approximately 0.283 radians or 16.24 degrees.
Step-by-step explanation:
To find the angle between two vectors, you can use the dot product formula:
cos(theta) = (u dot v) / (|u| * |v|)
Given u = 2i - 3j + k and v = i - 2j + k, we can calculate their dot product and magnitudes:
u dot v = (2 * 1) + (-3 * -2) + (1 * 1) = 2 + 6 + 1 = 9
|u| = sqrt((2^2) + (-3^2) + 1^2) = sqrt(4 + 9 + 1) = sqrt(14)
|v| = sqrt((1^2) + (-2^2) + 1^2) = sqrt(1 + 4 + 1) = sqrt(6)
Now we can calculate the angle:
cos(theta) = (9) / (√14 * √6) ≈ 0.959
theta = cos^{-1}(0.959) ≈ 0.283 radians ≈ 16.24 degrees